# Load packages

# Core
library(tidyverse)
library(tidyquant)

Goal

Visualize and compare skewness of your portfolio and its assets.

Choose your stocks.

from 2012-12-31 to 2017-12-31

1 Import stock prices

symbols <- c("BAC", "NOK", "NVDA", "F", "T")

prices <- tq_get(x = symbols,
                 get = "stock.prices",
                 from = "2012-12-31",
                 to = "2017-12-31")

2 Convert prices to returns (monthly)

asset_returns_tbl <- prices %>%
    
    group_by(symbol) %>%
    
    tq_transmute(select = adjusted,
                 mutate_fun = periodReturn, 
                 period = "monthly",
                 type = "log") %>%
    
    slice(-1) %>%
    
    ungroup() %>%

    set_names(c("asset", "date", "returns"))

3 Assign a weight to each asset (change the weigting scheme)

symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "BAC"  "F"    "NOK"  "NVDA" "T"
# weights
weights <- c(0.2, 0.2, 0.2, 0.2, 0.2)
weights
## [1] 0.2 0.2 0.2 0.2 0.2
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 BAC         0.2
## 2 F           0.2
## 3 NOK         0.2
## 4 NVDA        0.2
## 5 T           0.2

4 Build a portfolio

# tq_portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col = asset,
                 returns_col = returns,
                 weights = w_tbl,
                 rebalance_on = "months")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date       portfolio.returns
##    <date>                 <dbl>
##  1 2013-01-31           0.00459
##  2 2013-02-28          -0.00703
##  3 2013-03-28           0.0102 
##  4 2013-04-30           0.0379 
##  5 2013-05-31           0.0499 
##  6 2013-06-28          -0.00160
##  7 2013-07-31           0.0627 
##  8 2013-08-30          -0.0202 
##  9 2013-09-30           0.117  
## 10 2013-10-31           0.0505 
## # ℹ 50 more rows

5 Compute Skewness

portfolio_skew_tidyquant_builtin_percent <- portfolio_returns_tbl %>%
    
    tq_performance(Ra = portfolio.returns,
                   performance_fun = table.Stats) %>%

    select(Skewness)

portfolio_skew_tidyquant_builtin_percent
## # A tibble: 1 × 1
##   Skewness
##      <dbl>
## 1    0.343

6 Plot: Skewness Comparison

Histogram of expected returns and Risk

# Calculate sd of portfolio returns
sd_portfolio <- sd(portfolio_returns_tbl$portfolio.returns)
mean_portfolio <- mean(portfolio_returns_tbl$portfolio.returns)

portfolio_returns_tbl %>%
    
    mutate(extreme_neg = ifelse(portfolio.returns < mean_portfolio - 2 * sd_portfolio, 
                                "ext_neg",
                                "not_ext_neg")) %>%
    
    ggplot(aes(x = portfolio.returns, fill = extreme_neg)) +
    geom_histogram(binwidth = 0.003) +
    scale_x_continuous(breaks = seq(-0.06, 0.06, 0.02)) +
    labs(x = "monthly returns")

Scatterplot of skewness comparison

# Data transformation: calculate skewness
asset_skewness_tbl <- asset_returns_tbl %>%
    
    group_by(asset) %>%
    summarize(skew = skewness(returns)) %>%
    ungroup() %>%

    # Add portfolio skewness
    add_row(tibble(asset = "Portfolio",
                   skew = skewness(portfolio_returns_tbl$portfolio.returns)))
    
asset_skewness_tbl
## # A tibble: 6 × 2
##   asset       skew
##   <chr>      <dbl>
## 1 BAC       -0.159
## 2 F         -0.224
## 3 NOK        1.42 
## 4 NVDA       0.899
## 5 T         -0.263
## 6 Portfolio  0.343
# Plot skewness
asset_skewness_tbl %>%
    
    ggplot(aes(x = asset, y = skew, color = asset)) +
    geom_point() +
    
    ggrepel::geom_text_repel(aes(label = asset), 
                             data = asset_skewness_tbl %>%
                                 filter(asset == "Portfolio")) +
    
    labs(y = "skewness")

Rolling Skewness

# Transform data: calculate rolling skewness
rolling_skew_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select = portfolio.returns,
              mutate_fun = rollapply, 
              width = 24, 
              FUN = skewness,
              col_rename = "Skew") %>%
    
    select(-portfolio.returns) %>%
    na.omit()

# Plot
rolling_skew_tbl %>%
    
    ggplot(aes(x = date, y = Skew)) +
    geom_line(color = "cornflowerblue") +
    
    geom_hline(yintercept = 0, linetype = "dotted", linewidth = 2) +

    # Formatting
    scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, 0.2)) +
    theme(plot.title = element_text(hjust = 0.5)) +

    # Labeling
    labs(y = "skewness",
         x = NULL,
         title = "Rolling 24-Month Skewness") +
    
    annotate(geom = "text",
             x = as.Date("2016-07-01"), y = 0.8,
             color = "red", size = 5,
             label = str_glue("Rolling skewness is mostly positive, 
                              and is consistent with overall positive skewness"))

Is any asset in your portfolio more likely to return extreme positive returns than your portfolio collectively? Discuss in terms of skewness. You may also refer to the distribution of returns you plotted in Code along 4.

NOKIA has an abnormally higher skewness than all other inputted stocks. Following close second in NVIDIA. Comparing to the portfolio, no other ticker had a higher skewness than the portfolio. Therefore, NOK has the highest chance of positive returns, and T has the highest chance of negative returns based off skewness.